who profits from patents? rent-sharing at innovative …

WHO PROFITS FROM PATENTS? RENT-SHARING ATINNOVATIVE FIRMS∗

PATRICK KLINE

NEVIANA PETKOVA

HEIDI WILLIAMS

OWEN ZIDAR

This article analyzes how patent-induced shocks to labor productivity prop-agate into worker compensation using a new linkage of U.S. patent applicationsto U.S. business and worker tax records. We infer the causal effects of patent al-lowances by comparing firms whose patent applications were initially allowed tothose whose patent applications were initially rejected. To identify patents thatare ex ante valuable, we extrapolate the excess stock return estimates of Koganet al. (2017) to the full set of accepted and rejected patent applications based onpredetermined firm and patent application characteristics. An initial allowance ofan ex ante valuable patent generates substantial increases in firm productivityand worker compensation. By contrast, initial allowances of lower ex ante valuepatents yield no detectable effects on firm outcomes. Patent allowances lead firmsto increase employment, but entry wages and workforce composition are insensi-tive to patent decisions. On average, workers capture roughly 30 cents of everydollar of patent-induced surplus in higher earnings. This share is roughly twice as

∗We are very grateful to Joey Anderson, Ivan Badinski, Jeremy Brown,Alex Fahey, Sam Grondahl, Stephanie Kestelman, Tamri Matiashvili, MahnumShahzad, Karthik Srinivasan, and John Wieselthier for excellent research as-sistance and to Daron Acemoglu, Lawrence Katz, Bentley MacLeod, John VanReenen, four anonymous referees, and seminar participants at Brown, Dartmouth,the LSE/IFS/STICERD seminar, Michigan, Michigan State, MIT, NBER LaborStudies, NBER Productivity, Northwestern, NYU, Princeton, Stanford, StanfordGSB, the Toulouse Network for Information Technology, UC-Berkeley, UC-Irvine,UIUC, Chicago Booth, and the Washington Center for Equitable Growth for help-ful comments. The construction of some of the data analyzed in this article wassupported by the National Institute on Aging and the NIH Common Fund, Of-fice of the NIH Director, through Grant U01-AG046708 to the National Bureau ofEconomic Research (NBER); the content is solely the responsibility of the authorsand does not necessarily represent the official views of the NIH or NBER. Thiswork/research was also funded by the Ewing Marion Kauffman Foundation; thecontents of this publication are solely the responsibility of the grantee. Finan-cial support from the Alfred P. Sloan Foundation, NSF Grant nos. 1151497 and1752431, the Washington Center for Equitable Growth, the Kathryn and GrantSwick Faculty Research Fund, and the Booth School of Business at the Universityof Chicago are also gratefully acknowledged. Opinions expressed in the article donot necessarily represent the views and policies of the U.S. Department of theTreasury.

C© The Author(s) 2019. Published by Oxford University Press on behalf of Presidentand Fellows of Harvard College. All rights reserved. For Permissions, please email:[email protected] Quarterly Journal of Economics (2019), 1343–1404. doi:10.1093/qje/qjz011.Advance Access publication on March 27, 2019.

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1344 THE QUARTERLY JOURNAL OF ECONOMICS

high among workers present since the year of application. These earnings effectsare concentrated among men and workers in the top half of the earnings distribu-tion and are paired with corresponding improvements in worker retention amongthese groups. We interpret these earnings responses as reflecting the capture ofeconomic rents by senior workers, who are most costly for innovative firms toreplace. JEL Codes: J01, O3, O34.

I. INTRODUCTION

Competitive models of labor markets are predicated on thenotion that firms have no power to set wages. However, thereis mounting empirical evidence that firms contribute substan-tially to wage inequality among identically skilled workers (Card,Heining, and Kline 2013; Barth et al. 2016; Jager 2015; Card,Cardoso, and Kline 2016; Goldschmidt and Schmieder 2017;Helpman et al. 2017; Abowd, McKinney, and Zhao 2018; Sorkin2018; Song et al. 2019). This emerging evidence has renewed in-terest in mechanisms through which variation in firm produc-tivity can influence worker pay (see Lentz and Mortensen 2010;Manning 2011 for reviews).

While a sizable empirical literature has documented thatfluctuations in firm performance and worker compensation arestrongly related (Card et al. 2018), these correlations are opento widely varying interpretations. Early studies (e.g., Christofidesand Oswald 1992; Blanchflower, Oswald, and Sanfey 1996) esti-mated industry-level relationships that could simply reflect com-petitive market dynamics. A second generation of studies (VanReenen 1996; Hildreth 1998; Abowd, Kramarz, and Margolis1999) used firm-level data to study how shocks to firm perfor-mance translate into worker pay but was unable to adjust for po-tential changes in worker composition. More recent work (Guiso,Pistaferri, and Schivardi 2005; Card, Devicienti, and Maida2014; Lamadon 2014; Card, Cardoso, and Kline 2016; Carlsson,Messina, and Skans 2016; Mogstad, Setzler, and Lamadon 2017;Friedrich et al. 2019) adjusts for composition biases by examiningthe comovement between changes in firm productivity and thewage growth of incumbent workers. However, observational fluc-tuations in standard labor productivity measures are likely to re-flect a number of factors (e.g., market-wide fluctuations in productdemand, changes in nonpecuniary firm amenities, drift in labormarket institutions) that can influence wages without necessarilysignaling a violation of price-taking behavior by firms.

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WHO PROFITS FROM PATENTS? 1345

In this article, we analyze how patent-induced shocks tofirm performance propagate into worker compensation. Patentallowances offer a useful source of variation because they providefirms with well-defined monopoly rights that can yield a prolongedstream of potentially substantial economic rents. Standard mod-els of frictional labor markets (e.g., Pissarides 2000, 2009; Halland Milgrom 2008) suggest that these product market rents willbe shared with workers whenever the employment relationship is(re)negotiated, yet surprisingly little is known about how broadlypatent-generated rents are shared in practice.

Our analysis relies on a new linkage of two data sets:(i) the census of published patent applications submitted to theU.S. Patent and Trademark Office (USPTO) between roughly 2001and 2011 and (ii) the universe of U.S. Treasury business tax fil-ings and worker earnings histories drawn from W2 and 1099 taxfilings. The business tax filings data offers a high-quality set offirm-level variables, from which we are able to construct multiplemeasures of firm performance. Likewise, the business and workertax filings provide a window into compensation outcomes for manydifferent types of workers, including firm officers and owners, whoprevail at the top of the income distribution (Smith et al. 2019).

We infer the causal effect of patent allowances by comparingfirms whose applications were initially allowed to those whose ap-plications were initially rejected. Within so-called art units (tech-nological areas designated by the USPTO), firms with initiallyallowed and initially rejected applications submitted in the sameyear are found to exhibit similar levels and trends in outcomesprior to their initial patent decision. We also document that initialpatent decisions are difficult to predict based on firm character-istics or geography, corroborating the view that these decisionsconstitute truly idiosyncratic (as opposed to market-level) shocks.

It is well known that most patents generate little ex postvalue to the firm (Pakes 1986; Hall, Jaffe, and Trajtenberg 2001).We build on insights from two recent studies to identify a sub-sample of valuable patents that induce meaningful shifts in firmoutcomes at the time the patents are allowed. First, following thework of Farre-Mensa, Hegde, and Ljungqvist (2017), we restrictour analysis to firms applying for a patent for the first time, forwhich patent decisions are likely to be more consequential. Sec-ond, among this sample of first-time applicants, we build on theanalysis of Kogan et al. (2017) who use event studies to estimatethe excess stock market return realized on the grant date of U.S.

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patents assigned to publicly traded firms. Specifically, we developa methodology for extrapolating Kogan et al.’s patent value es-timates to the nonpublicly traded firms in our sample, and tofirms whose patent applications are never granted. We use char-acteristics of firms and their patent applications that are fixedat the time of application as the basis for extrapolating patentvalues and show that these value estimates are strong predic-tors of treatment effect heterogeneity in our sample. These valueestimates also provide us with an additional validation of our re-search design: patents with low predicted value are found to haveeconomically small and statistically insignificant effects on firmperformance and worker compensation.

Using these data, we investigate the consequences of obtain-ing an ex ante valuable patent allowance for firm performanceand worker compensation, and relate our findings to different ex-planations for the propagation of firm-specific shocks into workerwages. Corroborating recent research based on U.S. Census data(Balasubramanian and Sivadasan 2011), we find that firm sizeand average labor productivity rise rapidly in response to initialallowances of ex ante valuable patents. The average wage andsalary income of workers at these firms rises in tandem withmeasures of average labor productivity. An allowance of a patentapplication in the top quintile of ex ante predicted value raisesfirm-level surplus—defined as the sum of W2 earnings and busi-ness earnings before interest, taxes, and depreciation—by roughly$12,400 per W2 employee per year, while W2 earnings at the firmrise by approximately $3,700 per worker per year.

Patent allowances not only raise average earnings at assigneefirms but also exacerbate within-firm inequality on a variety ofmargins. Earnings impacts are heavily concentrated among em-ployees in the top quartile of the within-firm earnings distri-bution and among employees listed on firm tax returns as firmofficers. Likewise, we find that the earnings of owner-operatorsrise more than those of other employees. Earnings of male em-ployees rise strongly in response to a patent allowance, andthe earnings of female employees are less responsive to patentdecisions.

A handful of previous studies have investigated how inven-tor wages change in response to patent applications or patentgrants (Toivanen and Vaananen 2012; Depalo and Di Addario2014; Aghion et al. 2018; Bell et al. 2019). Consistent with theseresults, we find that the earnings of “inventors”—defined as

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employees ever listed as inventors on a patent application as inBell et al. (2019)—respond to patent allowance decisions. Inventorearnings are more responsive to patent allowance decisions thanare the earnings of noninventors, similar to the findings presentedin contemporaneous work by Aghion et al. (2018), which analyzeshow inventor and noninventor earnings in Finnish firms evolvebefore and after patent applications are filed.

Although these impacts on firm aggregates could, in princi-ple, be confounded by compositional changes, we find no evidencethat innovative firms upgrade the quality of their workforce inresponse to patent allowances. Although patent allowances leadfirms to expand by hiring slightly younger workers, the averageprior earnings of both new hires and firm separators is unaffectedby patent decisions, suggesting that there are no major changesin the skill composition of worker inflows to or outflows from thefirm on a year-to-year basis.

Different theoretical frameworks offer divergent predictionsabout how firm-specific shocks will affect the wages of new and in-cumbent workers. Empirically, the earnings of workers who wereemployed by the firm in the year of application respond verystrongly to patent decisions. Having a valuable patent allowedraises the average earnings of these “firm stayers” by roughly$7,800 (approximately 11%) a year. These gains appear to be con-centrated among firm stayers who, in the year of application, werelocated in the top half of the firm’s earnings distribution. We alsofind that the earnings of male firm stayers respond more stronglyto patent allowances than those of female firm stayers, which areestimated to be positive, albeit somewhat imprecise. By contrast,we are unable to detect any response of entry wages to patent al-lowances, which is inconsistent with the predictions of both staticwage-posting models and traditional bargaining models involv-ing Nash-style surplus splitting at the time of hiring (Pissarides2000, 2009; Hall and Milgrom 2008). While some dynamic wage-posting models (e.g., Postel-Vinay and Robin 2002) can generatedrops in entry wages in response to a productivity increase, thesemodels predict greater wage growth for new hires, a phenomenonfor which we also find no evidence. A candidate explanation forsuch “insider/outsider” distinctions in earnings impacts is thatthe wage fluctuations of incumbent workers represent changes inmarket perceptions of a worker’s underlying ability (Gibbons andMurphy 1992; Holmstrom 1999). However, we find much smallerand statistically insignificant earnings effects for workers who

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leave the firm, suggesting that our results are unlikely to be drivenby public learning about worker quality.

To interpret our findings, we sketch a simple model in whichincumbent workers are imperfectly substitutable with new hires.As in Becker (1964), Stevens (1994), and Manning (2006), thismechanism provides an avenue for incumbents to extract rentsfrom the firm in the form of wage premia. Motivated by this frame-work, we fit a series of “rent-sharing” specifications analogousto standard cost-price pass-through specifications used to studyimperfect competition in product markets (Goldberg and Heller-stein 2013; Weyl and Fabinger 2013; Gorodnichenko and Talavera2017). Using patent decisions as an instrument for firm surplus,we find that worker earnings rise by roughly 29 cents of everydollar of patent allowance-induced surplus, with an approximateelasticity of 0.35, which is comparable to the earlier estimatesof Abowd and Lemieux (1993) and Van Reenen (1996) that werebased on firm-level aggregates. Importantly, failing to instrumentfor surplus yields smaller elasticities, closer to those in the recentstudies reviewed by Card et al. (2018) that assume statistical in-novations to average labor productivity constitute structural pro-ductivity shocks. Consistent with our model, rent-sharing withfirm stayers is more pronounced than it is with average workers:stayers capture roughly 61 cents of every dollar of surplus for anapproximate elasticity of 0.56. When we exclude employees everlisted as inventors on a patent, pass-through to firm stayers fallsto roughly 48 cents with a corresponding elasticity of 0.5. Thoughthis elasticity estimate is larger than what has been found by mostprevious studies, its 90% confidence interval encompasses manyestimates in the literature.

In our model, firms share rents with incumbent workers toincrease the odds of retaining them. We provide event study evi-dence that retention rises in response to patent allowances, withlarger responses among workers in the top half of the earningsdistribution. The fact that groups experiencing the largest earn-ings responses exhibit the largest retention responses stronglysuggests that the earnings fluctuations we measure constituterents, rather than, say, risk-sharing arrangements that holdworkers to a participation constraint (Holmstrom 1979, 1989).Using the patent decision as an instrument for wages, we es-timate a retention-wage elasticity of roughly 1.2, with a 90%confidence interval ranging from 0.46 to 3.08. When convertedto a separation-wage elasticity, our point estimate lies near the

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middle of the range of quasi-experimental estimates reviewed inManning (2011).

Viewed through the lens of our model, our point estimatesimply that incumbent workers capture roughly 73% of their re-placement costs in wage premia. We estimate that the marginalreplacement cost of an incumbent worker at a firm receiving apatent allowance is roughly equal to a new hire’s annual earnings.These findings suggest that separations of key personnel can beextremely costly to innovative firms, even when these employeesare not themselves inventors. More broadly, our results suggestthat the influence of firm conditions on worker wages dependscritically on their degree of replaceability, which may be influ-enced by the duration of the relationship between the worker andfirm and a worker’s position within the firm hierarchy, issues em-phasized in recent empirical studies of wage setting at Europeanfirms by Buhai et al. (2014), Jager (2015), and Garin and Silverio(2017). In contrast with European settings, the legal barriers tohiring and firing workers are comparatively minimal for the setof newly innovative U.S. firms that are the focus of our analysis.The fact that seniority appears to mediate the propagation of firmshocks into worker earnings even in this sample of firms stronglysuggests an important role for relationship-specific investmentsin the generation of labor market rents.

II. INTERPRETING WAGE FLUCTUATIONS

In this section, we sketch a simple model of wage determi-nation designed to interpret the propagation of firm-specific pro-ductivity shocks into wages. Our model is tailored to the newlyinnovative firms that are the focus of our empirical analysis. Forthe purposes of motivating our model, two features of these firmsare notable. First, these firms are relatively small: the medianfirm in our estimation sample employs 17 workers in the yearof its first patent application.1 Such firms seem unlikely to pos-sess significant market power over new hires or have reputationsthat allow them to credibly commit to backloaded compensationschemes. Second, the innovative work conducted at these firms is

1. Although the firms in our sample are small relative to, say, firms includedin the Compustat data, they should not be thought of as anomalously small in size.Axtell (2001) finds using economic census data that the modal U.S. firm size is oneemployee, and the median is three (four if size-zero firms are not counted).

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necessarily specialized and proprietary in nature, likely makingit costly to replace incumbent employees with new hires. As inBecker (1964), Stevens (1994), and Manning (2006), the imperfectsubstitutability of incumbent workers with new hires provides anavenue for incumbent workers to extract rents from the firm inthe form of wage premia.

Our model yields a linear wage-setting rule similar tothose found in many search models with multilateral bargaining(Pissarides 2000; Cahuc and Wasmer 2001; Acemoglu andHawkins 2014), as well as in much of the classic literature onunion wage bargaining (Brown and Ashenfelter 1986). We use thisframework to motivate standard empirical “rent-sharing” speci-fications and clarify the endogeneity problems that arise whenestimating the transmission of firm-specific shocks to wages. Wethen discuss the assumptions under which patent allowance de-cisions can facilitate the identification of economic parameters ofinterest.

II.A. Preliminaries

We work with a one-period model. Each firm j ∈ {1, ..., J} be-gins the period with Ij incumbent workers and a nonwage amenityvalue Aj capturing factors such as geographic location and workenvironment. The firm can hire as many new workers as desired atcompetitive market wage wm

j = wm(Aj). As in classic hedonic mod-els (e.g., Rosen 1986), the wage demanded by new hires will tend tobe decreasing in the value of these amenities (i.e., ∂

∂ Ajwm(Aj) � 0),

which leads entry wages to vary by firm despite the perfectly com-petitive nature of this market.

Hiring Nj new workers requires paying a training and re-cruiting cost c (Nj, Ij). The function c (., .) exhibits constant returnsto scale, which implies

c(Nj, Ij

) = c(

Nj

Ij

)Ij .

We assume c (.) is twice differentiable and convex.The firm chooses a wage wI

j � wmj for incumbent workers at

the beginning of the period. After the wage is posted, incumbentworkers receive outside job offers. These offers are nonverifiable,in part because they may involve nonwage amenities and there-fore cannot be matched. However, the firm knows the offers havewage-equivalent values drawn from the following translated beta

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distribution

Gj (ω) =(

ω − wmj

w j − wmj

)η

for ω ∈ [wm

j , w j],

where w j > wmj is the maximum value of an outside offer. As

η grows, offers become concentrated around w j , while as η tendstoward 0, offers become concentrated around wm

j .Workers receiving outside offers with value greater than the

incumbent wage separate from the firm. Consequently, Gj(wIj )Ij

incumbent workers are retained for production activities. Notethat η can therefore be interpreted as the elasticity of workerretention with respect to the incumbent wage premium wI

j − wmj .

At the end of the period, the firm produces Qj = TjLj unitsof output where Lj = Nj + Gj(wI

j )Ij gives the number of retainedworkers and Tj gives the firm’s “physical” productivity. Outputis sold on a monopolistically competitive product market with

inverse product demand Pj(Qj) = P0j Q

− 1ε

j , where P0j > 0 is a firm-

specific constant capturing the firm’s product market power andε > 1 gives the elasticity of demand. After selling its output andpaying the retained workers, the firm shuts down.

II.B. The Firm’s Problem

The firm chooses the number of new hires Nj and an incum-bent wage wI

j to maximize profits. Formally, its problem is to:

max{wI

j ,Nj

} P0j

[Tj

(Gj

(wI

j

)Ij + Nj

)]1− 1ε︸︷︷︸

revenue

− c(

Nj

Ij

)Ij︸︷︷︸

training cost

− wmj Nj − wI

j G(wI

j

)Ij︸︷︷︸

wage bill

.

At an optimum, the firm equates the marginal cost of a newhire to her marginal revenue product (MRPj):

(1) wmj + c′

(Nj

Ij

)=

(1 − 1

ε

)P

(Qj

)Qj

Lj≡ MRPj.

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Note that the marginal cost of a hire exceeds the market wageby the amount of the training/recruiting cost c′

(Nj

Ij

), which is

increasing in the gross hiring rate Nj

Ij.

For incumbent wages, the first-order condition can be written:

(2) MRPj = wIj + wI

j − wmj

η︸︷︷︸inframarginal wage cost

.

As in monopsony models, the firm equates the marginal revenueproduct of an incumbent worker to her marginal factor cost, whichconsists of her wage wI

j plus a term capturing the costs of raisingwages for inframarginal incumbents. As the retention elasticityη approaches infinity, this term collapses to the standard neo-classical requirement that the marginal revenue product of anincumbent worker equal her wage.

II.C. Rent Sharing

Subtracting equations (1) and (2), we arrive at the followingexpression for the incumbent wage premium:

(3) wIj − wm

j = η

1 + ηc′

(Nj

Ij

).

Incumbents are paid a premium over new hires in propor-tion to their marginal training/recruiting costs c′

(Nj

Ij

). When

c′(

Nj

Ij

)= 0, incumbent workers are replaceable. In this case, the

firm views new hires and incumbents as perfect substitutes andpays them equivalently. The fraction η

1+η∈ [0, 1] plays the role

of the exploitation index in classic monopsony models (Manning2011) where η would correspond to a firm-specific labor supplyelasticity. As the retention elasticity η approaches infinity, incum-bents capture their full (marginal) replacement cost in the form ofelevated wages. As η tends toward 0, the outside options of incum-bents deteriorate, allowing the firm to retain them at the marketwage wm

j and capture the rents in the employment relationship.Plugging equation (3) into equation (1) yields an expression

for the incumbent wage that is useful for motivating our empirical

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rent-sharing specifications:

wIj = 1

1 + ηwm

j + η

1 + ηMRPj(4)

= (1 − θ ) wmj + θ MRPj,

where θ = η

1+η. Workers are paid a θ -weighted average of their

marginal productivity and the market wage wmj . Rewriting θ =

wIj −wm

j

MRPj−wmj

illustrates the link to models with Nash wage bargainingin which θ gives the fraction of marginal match surplus paid outin wage premia.2 As the retention elasticity η increases, θ risesand workers capture more of the surplus.

The parameter θ has a clear causal interpretation: a dollarincrease in marginal productivity yields a θ -cent pay increase forincumbents. It is useful to review briefly why marginal productscan vary in this model. In the special case where incumbents arereplaceable (c′

(Nj

Ij

)= 0), equation (1) implies the marginal rev-

enue product would be pinned to the market wage wmj . Hence,

there would be no scope for fluctuations in MRPj other than dueto shifts in the amenity vector Aj. But when incumbents are notreplaceable, MRPj will also respond to fluctuations in “revenueproductivity” P0

j Tj . As described below, our empirical approachuses variation in patent allowances to isolate the variation inMRPj that arises due to exogenous fluctuations in revenue pro-ductivity.

II.D. Estimating Pass-Through

We can operationalize equation (4) by plugging in the defini-tion of MRPj to get:

wIj = (1 − θ ) wm

j + θ

(1 − 1

ε

)Pj Qj

Lj

= (1 − θ ) wmj + πSj .(5)

2. Stole and Zwiebel (1996) propose a multilateral bargaining frameworkwhere workers and firms also bargain over inframarginal products. This bar-gaining concept is embedded in a search and matching framework by Acemogluand Hawkins (2014). Given our assumption of a constant product demand elas-ticity, the wage rule that results from the Stole-Zwiebel approach is analogous toequation (4) with the modification that the weights on the reservation wage andmarginal revenue product need not sum to 1.

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The last line of this expression is a standard empirical rent-sharing specification relating incumbent wages at the firm to ameasure of average labor productivity Sj = Pj Qj

Lj, which we refer

to as gross surplus per worker.The parameter π = θ

(1 − 1

ε

)governs pass-through of gross

surplus to wages and can be thought of as the labor mar-ket analog of cost-price pass-through coefficients often used tostudy imperfect competition in product markets (Goldberg andHellerstein 2013; Weyl and Fabinger 2013; Gorodnichenko andTalavera 2017). The term

(1 − 1

ε

)is an adjustment factor that

converts average labor productivity to marginal labor productiv-ity. While π is our primary parameter of interest, we also explorecalibrations of ε and consider the implied values of the structuralrent-sharing coefficient θ .

Card et al. (2018) review several studies that use panel meth-ods to assess the relation between the wage growth of incumbentworkers and fluctuations in various measures of firm surplus.Equation (5) suggests that such specifications will suffer fromomitted variables bias whenever surplus fluctuations are corre-lated with changes in the market wage wm

j . For example, shocksto firm productivity may contain a market-wide component. If allfirms in a market become more productive, market wages will rise.This possibility would lead to a misattribution of market-levelwage adjustments to rent-sharing and a corresponding upwardbias in OLS estimates of π .

A different class of potential biases arises from unobservedshocks to the amenity value of a firm. Suppose the work environ-ment at a firm improves and leads to a decrease in wm

j . This im-provement will lead, ceteris paribus, to an increase in firm scale,which will tend to depress average labor productivity throughdrops in the product price Pj(Qj). Consequently, such shocks will

induce a positive covariance between wmj and Sj = P0T

1− 1ε

j L− 1

ε

jand hence lead to an overstatement of the degree of rent-sharing.However, unobserved amenity shocks could also exert a direct ef-fect on productivity. For example, recent empirical literature findsthat variation in management practices affects worker moraleand productivity (Bloom and Van Reenen 2007; Bender et al.2018). A new manager who motivates workers could plausiblyraise total factor productivity Tj while lowering the market wagewm

j via increases in the amenity value Aj of the firm. This pos-sibility would lead to an underestimate of rent-sharing as the

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productivity shock is accompanied by an unobserved amenityshock.

II.E. Instrumenting with Patent Decisions

To circumvent these endogeneity problems, we use the ini-tial decision of the USPTO on a firm’s first patent applicationas an instrument for the firm’s surplus.3 Patents could influenceaverage labor productivity through two channels, both of whichprovide valid identifying variation. First, a patent grant couldraise a firm’s product price intercept P0

j by creating a barrier tocompetition by rival firms.4 Second, a patent grant could raise afirm’s TFP Tj by making it profitable for the firm to implementthe patented technology.

We document below that within observable strata, theUSPTO’s initial decision on a given patent application is unrelatedto trends in firm performance, suggesting that initial patent de-cisions are as good as randomly assigned with respect to counter-factual changes in firm outcomes. Consistent with this evidence,we also document below that it is hard to predict initial decisionsusing firm characteristics in the year of application. Finally, weassume that patent decisions are uncorrelated with fluctuationsin the market wage wm

j . In the model above, this condition is suf-ficient to ensure that instrumenting Sj with the patent allowanceisolates exogenous variation in revenue productivity P0

j Tj andidentifies the pass-through parameter π .

The assumption that patent decisions are uncorrelated withfluctuations in wm

j merits further discussion in our setting becauseseveral violations of this condition are conceivable, most of whichare not explicitly modeled in the above framework. A first concern

3. Van Reenen (1996) also investigated patents as a source of variation, butfound them to be a relatively weak predictor of firm profits in his sample of firms(see his note 11). This finding is in keeping with the notion that most patentsgenerate little ex post value to the firm (Pakes 1986), motivating our focus on exante valuable patent applications as described in Section V. A natural alternativeempirical strategy in our setting would be to use the leniency of the patent exam-iner assigned to review the patent application as an instrument, as in Sampat andWilliams (forthcoming). Unfortunately, this strategy reduces the precision of ourestimates to the point of being uninformative.

4. Perhaps the classic example is patents on branded small-molecule phar-maceuticals. In the absence of patents, many branded pharmaceuticals would ex-perience near-immediate entry of generic versions, which compete with brandedpharmaceuticals at close to marginal cost prices.

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is that patent allowances might lead the firm to demand morehours from workers, in which case wm

j would rise. However, wewould expect this to be a short-run phenomenon that dissipatesas the firm expands toward its new target size, and we find noevidence of such wage dynamics in the data. A different sort of vi-olation would occur if patents shift expectations about firm growthand therefore about the future earnings growth of workers. Thissort of mechanism arises in dynamic wage-posting models with of-fer matching (Postel-Vinay and Robin 2002) and would imply thatwm

j falls in response to an allowance. However, such a violationwould also imply that initial allowances should raise the wagegrowth of new hires, an assertion for which we find no empiricalsupport.

A second concern is that initial allowance decisions might begeographically correlated, in which case instrumenting with ini-tial allowances might pick up market-wide fluctuations in wm

j . Weshow that the intraclass correlation of initial patent allowanceswithin geography and sector is indistinguishable from 0, whichsuggests that allowances are best thought of as truly firm-specificshocks. We find no impact of patent allowances on the earningsof workers in their first year of employment with a firm, whichshould provide a reasonable proxy of the market wage wm

j . Becauseall of the above concerns involve correlations between patent al-lowances and fluctuations in the market wage wm

j , this providesa strong corroboration of the exogeneity of the patent allowanceinstrument.

A final concern is that firms may respond to patent decisionsby changing the composition of their workforce. By leveraging thepanel structure of our data, we can directly investigate whetherfirms change their composition of new hires (or separations) inresponse to patent allowances. We also address this concern byanalyzing the wage growth of incumbent workers, which by con-struction differences out any selection on time-invariant charac-teristics. In practice, we find that such adjustments have littleeffect on our estimates of the pass-through parameter π .

III. DATA AND DESCRIPTIVE STATISTICS

To conduct our empirical analysis, we construct a novel link-age of several administrative databases, which provides us withpanel data on the patent filings, patent allowance decisions, andoutcomes of U.S. firms and workers.

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III.A. USPTO Patent Applications

We begin with public-use administrative data on the uni-verse of patent applications submitted to the USPTO since late2000.5 We link these published U.S. patent applications with sev-eral USPTO administrative data sets. Because published patentapplications are not required to list the assignee (owner) of thepatent, approximately 50% of published patent applications wereoriginally missing assignee names. We worked with the USPTOto gain access to a separate public-use administrative data filethat allows us to fill in assignee names for most of these appli-cations. The public-use USPTO PAIR (Patent Application Infor-mation Retrieval) administrative data records the full correspon-dence between the applicant and the USPTO, allowing us to inferthe timing and content of the USPTO’s initial decision on eachpatent application and other measures of USPTO and applicantbehavior. Details on these and the other patent-related data filesthat we use are included in Online Appendix A.6

Table I, Panel A describes the construction of our patent appli-cation sample. Our full sample consists of the roughly 3.6 millionpatent applications filed on or after November 29, 2000, that werepublished by December 31, 2013; we restrict attention to applica-tions filed on or before December 31, 2010, to limit the impact ofcensoring. We drop around 400,000 applications that are missingassignee names and therefore cannot be matched to business taxrecords. We also limit our sample to standard (so-called utility)patents.7

To focus on a subset of firms for which patent allowancesare most likely to induce a meaningful shift in firm outcomes, wemake several restrictions that aim to limit our sample to first-time patent applicants. First, we drop so-called child applicationsthat are derived from previous patent applications. Second, weretain the earliest published patent application observed for each

5. The start date of our sample is determined by the American InventorsProtection Act of 1999, which required publication of nearly the full set of U.S.patent applications filed on or after November 29, 2000. We say “nearly” becauseour sample misses patent applications that opt out of publication; Graham andHegde (2014) use internal USPTO records to estimate that around 8% of USPTOapplications opt out of publication.

6. Please refer to the Online Appendix for all appendix materials.7. Utility patents, also known as “patents for invention,” comprise ap-

proximately 90% of USPTO-issued patent documents in recent years; seehttps://www.uspto.gov/web/offices/ac/ido/oeip/taf/patdesc.htm for details.

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https://www.uspto.gov/web/offices/ac/ido/oeip/taf/patdesc.htm


TABLE ISAMPLE CONSTRUCTION

Application-assignee pairs Applications Assignees EINs

Panel A: USPTO sampleFull sample 3,737,351 3,601,913 317,370 —Filed between 2000 and 2010 3,063,980 2,954,507 279,936 —Nonmissing assignees 2,708,829 2,599,373 279,935 —Nonchild applications 1,341,843 1,295,649 130,619 —Utility applications 1,339,146 1,293,054 130,113 —First application by assignee 130,113 125,018 130,113 —No prior grant to assignee 99,871 95,767 99,871 —

Panel B: USPTO-tax merge — 39,452 39,814 81,934First application by EIN — 37,714 — 81,877No prior grant to EIN — 35,643 — 78,291EIN with largest revenue — 35,643 — 35,643Active firms — 9,732 — 9,732

Notes. This table describes the construction of our analysis sample. When selecting the first applicationby each assignee by date of filing (“First application by assignee”), ties are broken by taking the smallestapplication number. When selecting the first application for each EIN (“First application by EIN”), we dropEINs with more than one first application. When removing assignees (“No prior grant to assignee”) and EINs(“No prior grant by EIN”) with prior grants, we do so by checking against the assignees and EINs for thecensus of patents granted since 1976 and filed before November 29, 2000. When selecting the EIN with thelargest revenue (“EIN with largest revenue”), we compare based on the revenue in the year of the application.Active firms are defined as EINs with nonzero/nonmissing total income or total deductions in the applicationyear and in the three previous years, a positive number of employees in the application year, and revenue lessthan $100 million in 2014 dollars.

assignee in our sample.8 Finally, we exclude assignees which weobserve to have had patent grants prior to the start of our pub-lished patent application sample.9 Ideally, we would exclude as-signees that had patent applications (not just patent grants) priorto the start of our published patent application sample, but un-successful patent applications filed before November 29, 2000, arenot publicly available. These restrictions leave a sample of around96,000 patent applications, which we then attempt to match to ourU.S. Treasury business tax files.

8. Because USPTO procedure assigns application numbers sequentially, webreak ties in the cases in which a given assignee submits multiple applications onthe same day by taking the smallest application number.

9. We search for such patent grants going back to 1976, the date after whichelectronic patent grant records are most easily available. Given the firms in oursample, the likelihood that a firm had a patent granted prior to 1976 seemedsufficiently small not to warrant a more extensive attempt to match to earlierpatent grants.

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III.B. Treasury Tax Files

We link Treasury business tax filings with worker-level fil-ings. Annual business tax returns record firm outcomes from Form1120 (C-corporations), 1120S (S-corporations), and 1065 (partner-ship) forms and cover the years 1997–2014. The key variables thatwe draw from the business tax return filings are revenue, valueadded, EBITD (earnings before interest, taxes, and deductions),and labor compensation; these are defined in more detail in OnlineAppendix A.

We link these business tax returns to worker-level W2 and1099 filings to measure employment and compensation for em-ployees (e.g., wage bill) and independent contractors, respectively,at the firm-year level. The relevant variables are defined in moredetail in Online Appendix A. We winsorize all monetary values inthe tax files from above and below at the 5% level, which is stan-dard when working with the population of U.S. Treasury businesstax files (see, for example, Yagan 2015; DeBacker et al. 2016).Since our analysis focuses on per-worker outcomes, we winsorizeoutcomes on a per-worker basis.

To distinguish employment and compensation for inventorsand noninventors, we use Bell et al.’s (2019) merge of inventorslisted in patent applications to W2 filings. Inventors are definedas individuals ever appearing in the Bell et al. (2019) patentapplication–W2 linkage, rather than individuals listed as inven-tors on the specific patent application relevant to a given firm inour sample.

III.C. Linkage Procedure

We build on the name standardization routine usedby the NBER’s Patent Data Project (https://sites.google.com/site/patentdataproject/) to implement a novel firm name–basedmerge of patent assignees to firm names in the U.S. Treasurybusiness tax files. Specifically, we standardize the firm names inboth the patent data and (separately) the Treasury business taxfiles to infer that, for example, “ALCATEL-LUCENT U.S.A., INC.,”“ALCATEL-LUCENT USA, INCORPORATED,” and “ALCATEL-LUCENT USA INC” are all the same firm. We then conduct afuzzy merge of standardized assignee names to standardized firmnames in the business tax files using the SoftTFIDF algorithmbased on a Jaro-Winkler distance measure. This merge is de-scribed in more detail in Online Appendix A.

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https://sites.google.com/site/patentdataproject/

https://sites.google.com/site/patentdataproject/


To assess the quality of our merge, we conduct two qualitychecks: first, we validate against a hand-coded sample; second, wevalidate against the inventor-based linkage of Bell et al. (2019).As described in Online Appendix A, the results of these validationexercises suggest that our merge is of relatively high quality, withtype I and II error rates on the order of 5%.

Table I, Panel B describes our linkage between the USPTOpatent applications data and the U.S. Treasury business tax files.Of the ∼96,000 patent applications we attempt to match to theU.S. Treasury business tax files, we match around 40,000 patentapplications. The USPTO estimates that in 2015 approximately49.6% of patent grants were filed by U.S.-based assignees, whichimplies our match rate to U.S.-tax-paying entities is on the order of83%.10 These 40,000 patent applications are matched to ∼40,000standardized firm names in the Treasury business tax files, whichcorrespond to 82,000 firms (employer identification numbers, orEINs).

We build the analysis sample from these 82,000 EINs in foursteps. Our goal here is to construct a unique and well-definedmatch between patent applications and firms in a subset of firmsfor which patent allowances are most likely to induce a mean-ingful shift in firm outcomes.11 First, we attempt to restrict ourpostmerge tax analysis sample to first-time patent applicants byretaining the earliest published patent application observed foreach EIN, and by excluding EINs which we observe to have hadpatent grants prior to the start of our published patent applicationsample. Second, in cases where there are multiple EINs for a stan-dardized name in the tax files, we keep the EIN with the largestrevenue in the year that the patent application was filed. Third,we restrict attention to “active” firms, defined as EINs with a pos-itive number of employees in the year of application and nonzero,nonmissing total income or total deductions in the year the patentapplication was filed and in the three previous years. This restric-tion allows us to investigate pretrends in our outcome variablesamong economically relevant firms. Fourth, we limit attention toEINs with less than US 100 million in revenue in 2014 dollars inthe year of patent application. This step, which eliminates firms

10. These USPTO estimates, which are based on the reported lo-cation of patent assignees, are available at https://www.uspto.gov/web/offices/ac/ido/oeip/taf/own_cst_utl.htm.

11. In Online Appendix B, we describe these sample restrictions in more detail.

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https://www.uspto.gov/web/offices/ac/ido/oeip/taf/own_cst_utl.htm

https://www.uspto.gov/web/offices/ac/ido/oeip/taf/own_cst_utl.htm


in the top centile of the firm size distribution, allows us to avoidcomplexities related to the largest multinational companies andfocus on firms for whom patent allowance decisions are more likelyto be consequential.12 These restrictions leave us with a sampleof 9,732 patent applications, each uniquely matched to one EINin the U.S. Treasury business tax files. It is worth noting thatfocusing on such a small subset of firms is common in analysessuch as ours. For example, Kogan et al. (2017) start with data on7.8 million granted patents, which they winnow down to a finalsample of 5,801 firms with at least one patent.

III.D. Measuring Surplus

As described in Card et al. (2018), empirical rent-sharing es-timates are often sensitive to a number of measurement issues,the most prominent of which is the choice of rent measure. Inkeeping with equation (5), we rely on a gross surplus measure ofrent that differs from “match surplus” due to the absence of dataon workers’ reservation wages. Letting �j denote the firm’s eco-nomic profits, the model of Section II implies the firm’s total grosssurplus can be written:

Sj Lj = wmj Nj + wI

j G(wI

j

)Ij︸︷︷︸

wage bill

+ � j︸︷︷︸profits

+ c(

Nj

Ij

)Ij︸︷︷︸

training/recruiting costs

.

To measure this theoretical concept in the tax data, we usethe sum of the firm’s W2 earnings in a year and its EBITD. Thoughfirms sometimes report negative EBITD, this surplus measure isusually positive and provides a plausible upper bound on the flowof resources capable of being captured by workers. Note that thismeasure is theoretically justified by the presumption that firmsdo not claim deductions on training costs; that is, that EBITDcaptures the sum � j + c

(Nj

Ij

)Ij .13

12. Statistics for firm size distribution are from Smith et al. (2019). Specifically,in the full population of C-corporations, S-corporations, and partnerships withpositive sales and positive W2 wage bills, $100 million in revenue in 2014 dollarsfalls in the top 1% of firms.

13. Unlike some other capital expenses and costs related to intangibles,which can be amortized, firms typically cannot amortize and deduct costs re-lated to training. Specifically, section 197 on intangibles includes workforcein place (e.g., “experience, education, or training”’) and business books and

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For comparison with past work, we also report results thatuse a value-added measure of surplus. Our approximation to valueadded comes from line 3 of Form 1120, which deducts both returnsand allowances and the cost of goods sold from gross sales. Thismeasure suffers from the disadvantage that it may include a num-ber of additional unobserved firm costs, including rents, advertis-ing, and financing fees, that are likely unavailable for capture byworkers.

III.E. Summary Statistics

Table II tabulates summary statistics on our firm and workeroutcomes in each of two samples: our analysis sample of matchedpatent applications/firms (N = 9,732), and our subsample ofmatched patent applications/firms for which the patent applica-tions are in the top quintile of predicted value (N = 1,946), whichwill be defined in the next section. All summary statistics are asof the year the patent application was filed.

Table II, Panel A documents summary statistics on firm-leveloutcomes. In our analysis sample, the median firm generatedaround $3 million in revenue, employed 17 workers, and reportedroughly $7,000 in EBITD per worker. Approximately 8% of patentapplications were initially allowed. Panel B documents summarystatistics on worker-level outcomes. The median firm in our anal-ysis sample paid $48,000 in annual earnings per W2 employee,employed a workforce that was approximately 75% male, and is-sued 2.5% of its W2s to individuals listed as inventors on at leastone patent application. Contract work turns out to be relativelyuncommon in this sample, with 1099s constituting only about 10%of the sum of W2 and 1099 employment for the median firm.

IV. INSTITUTIONAL CONTEXT: INITIAL PATENT DECISIONS

The USPTO is responsible for determining which (if any)inventions claimed in patent applications should be granted apatent. Patentable inventions must be patent-eligible (35 U.S.C.§101), novel (35 U.S.C. §102), nonobvious (35 U.S.C. §103), anduseful (35 U.S.C. §101), and the text of the application must sat-isfy the disclosure requirement (35 U.S.C. §112). When patent

records (e.g., “intangible value of technical manuals, training manuals, or pro-grams”) in the list of assets that cannot be amortized for most firms. Seehttps://www.irs.gov/pub/irs-pdf/p535.pdf for additional details.

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https://www.irs.gov/pub/irs-pdf/p535.pdf


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applications are submitted to the USPTO, they are routed to acentral office, which directs the application to an appropriate artunit that specializes in the technological area of that applica-tion. For example, art unit 1671 reviews applications related tothe chemistry of carbon compounds, whereas art unit 3744 re-views applications related to refrigeration. The manager of therelevant art unit assigns the application to a patent examiner forreview. If the examiner issues an initial allowance, the inventorcan be granted a patent. If the examiner issues an initial rejec-tion, the applicant has the opportunity to revise and resubmitthe application, and the applicant and examiner may engage inmany subsequent rounds of revision (see Williams 2017 for moredetails).

Our empirical strategy focuses on contrasting firms that re-ceive an initial allowance to other firms that applied for a patentbut received an initial rejection. Empirically, most patent appli-cations receive an initial decision within three years of being filed(see Online Appendix Figure D.1). While some applications thatare initially rejected receive a patent grant relatively quickly,the modal application that is initially rejected is never granteda patent (see Online Appendix Figure D.2).

Because our empirical strategy will contrast firms whose ap-plications are initially allowed with those whose applications areinitially rejected, having some sense of what predicts initial al-lowance decisions is useful. Table III reports least squares esti-mates of the probability of an initial allowance as a function offirm characteristics in the year of application. Column (1) showsthat predicting initial allowances is surprisingly difficult. Appli-cations from firms with more W2 employees are somewhat lesslikely to be initially allowed, as are those from firms with highervalue added per worker. Jointly, the covariates are statisticallysignificant. Column (2) adds art unit by application year fixed ef-fects that control for technology-specific changes over time. Thissimple addition renders all baseline covariates statistically in-significant both individually and jointly, which provides some as-surance that initial patent decisions are not strongly dependenton baseline firm performance. Given this empirical evidence, weproceed by assuming that any remaining selection is on time-invariant firm characteristics that can be captured by firm fixedeffects.

A separate concern has to do with whether initial allowancesare best thought of as idiosyncratic or market-level shocks.

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TABLE IIIBALANCE OF ASSIGNEE CHARACTERISTICS ACROSS INITIALLY ALLOWED AND INITIALLY

REJECTED PATENT APPLICATIONS

Initially allowed

Analysis sample Top quintile

(1) (2) (3) (4)

log (employees) − 3.71 − 2.06 − 0.16 1.97(1.85) (2.18) (4.70) (4.76)

Revenue per worker 0.03 0.02 0.01 0.01(0.01) (0.02) (0.02) (0.03)

Value added per worker − 0.14 − 0.07 − 0.07 0.00(0.05) (0.06) (0.08) (0.12)

Wage bill per worker 0.14 0.14 0.08 − 0.11(0.10) (0.13) (0.21) (0.24)

EBITD per worker 0.11 0.06 0.17 0.12(0.05) (0.07) (0.10) (0.14)

Observations 9,732 8,647 1,946 1,666AU-AY FEs

√ √

p-value .005 .494 .518 .830

Notes. This table reports covariate balance tests for initial patent allowances. Specifically, the coefficientsreport linear probability model estimates of the marginal effect of the included covariate on the probabilitythat a patent application receives an initial allowance; all coefficients have been multiplied by 1,000 for easeof interpretation. AU-AY FEs denotes the inclusion of art unit (AU) by application year (AY) fixed effects.Covariates are measured as of the year of application. Columns (1) and (2) report the results for observations inthe analysis sample. Columns (3) and (4) report the results for observations in the top-quintile predicted patentvalue. Singleton observations are dropped in the fixed effects specifications, which accounts for the smallernumber of observations in column (2) relative to column (1) and in column (4) relative to column (3). Standarderrors (reported in parentheses) are two-way clustered by art unit and application year by decision yearexcept in column (4) which clusters by art unit (because the estimated two-way variance covariance matrixwas singular). The p-value reports the probability that the covariates measured in the year of application donot influence the probability of an initial allowance. EBITD is earnings before interest, taxes, and deductions.Revenue, value added, wage bill, and EBITD are measured in thousands of 2014 dollars.

Seminal work by Jaffe, Trajtenberg, and Henderson (1993) demon-strated that patent citations are highly localized geographically.To test whether initial allowances are also geographically clus-tered, we fit linear random effects models to the initial allowancedecision. Online Appendix Table D.1 reports intraclass correla-tions at various levels of geography before and after subtract-ing off art unit by application year mean allowance rates. In ei-ther case, the within-state correlation is estimated to be 0, whilethe correlation within five-digit ZIP codes is quite low (0.06–0.07)and statistically indistinguishable from 0. These findings indicatethat initial allowances are best thought of as truly idiosyncratic

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firm-specific shocks that are unlikely to elicit market-wide wageresponses.

V. DETECTING VALUABLE PATENTS

The value distribution of granted patents is heavily skewed(Pakes 1986), which suggests that low-value patent applications—if granted—are unlikely to generate meaningful shifts in firm out-comes. Constructing a measure of the ex ante value of patent ap-plications enables us to focus our analysis on patent applicationsthat are likely to induce changes in firm behavior.

A variety of metrics have been proposed as measures ofthe value of granted patents, including forward patent cita-tions (Trajtenberg 1990), patent renewal behavior (Pakes 1986;Schankerman and Pakes 1986; Bessen 2008), patent owner-ship reassignments (Serrano 2010), patent litigation (Harhoff,Scherer, and Vopel 2003), and excess stock market returns(Kogan et al. 2017). These value measures encounter three chal-lenges in our empirical context. First, these measures are onlydefined for granted patents, whereas we would like to take ad-vantage of data on patent applications, including those that areultimately unsuccessful. Second, most of these measures arguablycorrespond to a measure of social value—or social spillovers, in thesense of social value minus private value—whereas we are moreinterested in measuring firms’ private value of a patent. This issuearises most sharply with forward patent citations, which are typ-ically used as a measure of spillovers (e.g., Bloom, Schankerman,and Van Reenen 2013). Third, all of these measures are defined expost: citations, renewals, reassignments, and litigation are oftenmeasured many years after the initial patent award. But in ourcontext (as in Kogan et al. 2017) what is arguably more relevant isthe expected private value of the patent at the time of the patentapplication or patent grant.

To this end, we build on the recent analysis of Kogan et al.(2017) (henceforth KPSS), who measure the high-frequency re-sponse of stock prices around the date of patent grant announce-ments to estimate the value of patent grants awarded to pub-licly traded companies. We estimate a simple statistical modeldesigned to extrapolate their estimates to nonpublicly tradedcompanies and to nongranted patent applications in our analysissample.

We model the KPSS patent value ξ j for each firm-patent ap-plication j in our data as obeying the following conditional mean

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restriction:

E[ξ j |Xj, A j

] = exp(X ′

jδ + νA j

),

where Xj denotes a vector of baseline firm and patent applica-tion covariates, and A j denotes the art unit to which the appli-cation was assigned. The exponential functional form underly-ing this specification is designed to accommodate the fact thatthe KPSS values are nonnegative and heavily skewed. Becausewe have, on average, only 2.3 applications with nonmissing ξ jper art unit, some penalization is required to avoid overfitting.Accordingly, we treat the art unit effects {νa} as i.i.d. drawsfrom a normal distribution with unknown variance σ 2

ν ratherthan fixed parameters to be estimated. The model is fit via arandom effects Poisson maximum likelihood procedure. As de-scribed in Online Appendix C, this procedure exploits the con-ditional mean restriction E[ξa|Xa] = ∫

exp(X ′aδ + ν)ωa (ν) dν where

ξa is the vector of KPSS values in an art unit a, Xa is the corre-sponding vector of baseline application and firm predictors, andωa(ν) is the posterior distribution of νa given the observed data(ξa, Xa).

To maximize statistical power, we relax the sample restric-tion that focused our main analysis on “active” firms, defined asEINs that have a positive number of employees in the year ofapplication and nonzero, nonmissing total income or total deduc-tions in the year the patent application was filed and in the threeprevious years. In our main analysis, that restriction allowed usto investigate pretrends in our outcome variables. By relaxingthat restriction here and including those firms in our Poisson es-timation, we gain precision and further reduce the potential foroverfitting problems to arise. In practice, the full sample size forour Poisson estimation is 596, of which 159 observations satisfythe active firm sample restriction.14

Table IV reports the Poisson parameter estimates. Appli-cations submitted to more countries (“patent family size”) tendto be of higher value, as do applications with more claims and

14. Recall that active firms are defined as EINs with nonzero/nonmissing totalincome or total deductions in the application year and in the three previous years,a positive number of employees in the application year, and revenue less than $100million in 2014 dollars.

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TABLE IVPREDICTION OF KPSS PATENT VALUE BASED ON PATENT APPLICATION AND ASSIGNEE

CHARACTERISTICS

KPSS value (ξ )

1(patent family size = 1) 0.28 (0.06)log (patent family size) 0.23 (0.04)1(number of claims = 1) 0.68 (0.19)log (number of claims) 0.30 (0.03)1(revenue = 0) 1.42 (0.14)log (revenue) 0.14 (0.02)1(employees = 0) 0.45 (0.07)log (employees) − 0.01 (0.02)Application year − 0.03 (0.05)(Application year)2 − 0.01 (0.01)Decision year 0.30 (0.06)(Decision year)2 − 0.03 (0.01)Constant − 1.40 (0.21)log(σν ) 0.24 (0.05)

Observations 596Art units 260χ2 10,353

Notes. This table reports the relationship between KPSS ξ patent value, and patent application and firm-level covariates. Coefficient estimates are from a Poisson model with art unit random effects. The sample isthe subsample of granted patents for which the Kogan et al. (2017) measure of patent value is available in ouranalysis sample, except we retain firms with more than $100 million in 2014 revenue (unlike in our analysissample) to maximize sample size (N = 596). The dependent variable is the KPSS measure of patent value ξ inmillions of 1982 dollars. Standard errors are reported in parentheses. Patent family size measures the numberof countries in which the patent application was submitted. Number of claims measures the number of claimsin the published U.S. patent application. Revenue (in thousands of 2014 dollars) and number of employeesare measured as of the year the patent application was filed. log(σν ) reports the log of the estimated standarddeviation of the art unit random effects. χ2 reports the results of a likelihood ratio test statistic against arestricted Poisson model without art unit random effects; this test has 1 degree of freedom.

applications submitted by firms with larger revenues.15 We alsodocument substantial variability of patent value across art units:a standard deviation increase in the art unit random effect is esti-mated to raise mean patent values by e0.24 × 100 = 127 log points.This variability finding is of interest in its own right because it

15. The number of countries to which an application was submitted, often re-ferred to as patent “family size,” is defined as a set of patent applications filed withdifferent patenting authorities (e.g., the United States, Europe, Japan) that referto the same invention; work starting with Putnam (1996) has argued that firmsshould be willing to file more privately valuable patents in a larger number of coun-tries. Patents list “claims” over specific pieces of intellectual property, and workstarting with Lanjouw and Schankerman (2001) has argued that patents with alarger number of claims may be more privately valuable. See Online Appendix Afor details on both these measures.

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FIGURE I

KPSS Value (ξ): Predicted versus Actual

This figure is a binned scatterplot of actual versus predicted values of the KPSSmeasure of patent value ξ in millions of 1982 dollars. The sample is the subset ofpatent applications with nonmissing values for the KPSS measure of patent valueξ . Predictions are formed based on estimates from the random effects Poissonmodel described in Section V. The data in this figure have been grouped into20 equal-sized bins. In the microdata, the slope is 1.12, as reported in the text.Here, the coefficient β instead reports the 2SLS slope using 20 bin dummies asinstruments for predicted values and “se” reports the associated standard error.

suggests that patent decisions involve much higher stakes in someUSPTO art units than others.

We use our estimates of the parameters (δ, σ ν) to computeempirical Bayes predictions ξ j of ξ j for every patent application inour analysis sample, including those that lack a KPSS value eitherbecause the application is assigned to a privately held firm orbecause the application is never granted a patent.16 Empirically,these predictions are highly accurate: a least squares fit of ξ j to ξ jyields a slope of 1.12 and an R2 of 68%. Figure I shows that binnedaverage KPSS values track the empirical Bayes predictions veryclosely. Online Appendix Table D.2 lists mean predicted values bysubject matter area.

16. In cases where no valid KPSS values are present in the entire art unit, weform our prediction by imputing an art unit random effect of 0.

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The ultimate test of ξ j is whether it predicts treatment ef-fect heterogeneity: that is, do allowances of patent applications ofhigher predicted value result in larger shifts in firm outcomes? Toinvestigate this question, we fit a series of interacted difference-in-differences models of the following form:

(6) Yjt = α j + κt,k( j) + Postjt ·[

5∑b=1

sb(ξ j

) · (ψb + τb · I Aj

)] + rjt,

where Yjt is an outcome for firm (EIN) j in year t, αj are firmfixed effects, and κ t,k( j) are calendar year fixed effects that varyby art unit/application year cell k( j). The variable Postjt is anindicator for having received an initial patent decision, IAj is anindicator for whether the patent application is initially allowed,and {sb (.)}5

b=1 is a set of basis functions defining a natural cubicspline with five knots.17 Intuitively, this specification comparesinitially allowed and initially rejected applications in the sameart unit by application year cell, before and after the date of theinitial decision. The spline interactions allow the effects of aninitial allowance to vary flexibly with the predicted patent valueξ j .

Of primary interest is the “dose-response” function d (x; τ ) ≡∑5b=1 sb (x) τb, which gives the effect of an initial allowance for a

patent with predicted value x. Figure II plots our estimates ofthis function for a grid of values x when Yjt is either surplusper worker or wage bill per worker. In these cases, we find evi-dence of an S-shaped response: impacts of initial allowances onboth wages and surplus are small and statistically insignificant atlow predicted value levels, corroborating both the exclusion andrandom assignment assumptions underlying our research design.Patents with ex ante predicted patent values above $5 million in1982 dollars—roughly the 80th percentile of the predicted valuedistribution—have larger, statistically significant treatment

17. The natural cubic spline is a cubic b-spline that imposes continuous secondderivatives everywhere but allows the third derivative to jump at the knots (seeHastie, Tibshirani, and Friedman 2016 for discussion). Following Harrell (2001),we space knots equally at the 5th, 27.5th, 50th, 72.5th, and 95th percentiles ofthe distribution of patent values, which correspond to dollar values of roughly$0.1M, $0.7M, $1.7M, $4.1M, and $19.0M 1982 dollars, respectively. The spline isconstrained to be linear below the 5th and above the 95th percentiles.

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FIGURE II

Impacts by Predicted Patent Value: Surplus and Wage Bill

This figure shows the impact of an initial patent allowance on surplus per workerand wage bill per worker as a function of predicted patent value in our analysissample. The vertical red line (color version online) is the cut-off value for thetop-quintile predicted patent value subsample and is equal to $5.3 million in1982 dollars. Values along the x-axis for the surplus series are offset from theirinteger value to improve readability. Surplus is EBITD (earnings before interest,tax, and depreciation) + W2 wage bill. 95% confidence intervals shown are basedon standard errors two-way clustered by (i) art unit and (ii) application year bydecision year.

effects that increase rapidly before stabilizing at values near $12million in 1982 dollars.18

Given the S-shaped pattern of treatment effect heterogeneitydocumented in Figure II, our empirical analysis pools the bot-tom four quintiles together and focuses on estimating the impactsof patents in the top quintile of ex ante predicted patent value.Reassuringly, Table III, columns (3) and (4) show that initial al-lowances are equally difficult to predict with baseline character-istics within the top quintile of predicted value, especially afterart unit by application year fixed effects have been included. Like-wise, columns (3a)–(4b) of Online Appendix Table D.1 show thatamong top-quintile applications, initial allowances continue notto exhibit spatial correlation.

18. We reference 1982 dollars because those are the units used by KPSS.

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VI. REDUCED-FORM ESTIMATES

The treatment effect heterogeneity documented in Figure IIdemonstrates that firms experience economically and statisticallysignificant increases in profitability and wages when valuablepatent applications are allowed. However, a natural concern isthat these findings could reflect preexisting trends rather thancausal effects of the patent decisions. To investigate this concern,we estimate a series of “event study” specifications of the followingform:

Yjt = α j + κt,k( j) + Q5 j ·[ ∑

m∈MDm

jt · (ψ5,m + τ5,m · I Aj

)](7)

+ (1 − Q5 j

) ·[ ∑

m∈MDm

jt · (ψ<5,m + τ<5,m · I Aj

)] + rjt,

where Q5j is an indicator for the firm’s patent application beingin the top quintile of predicted ex ante value, Dm

jt is an indica-tor for firm j’s decision having occurred m years ago, and theset M = {−5,−4,−3,−2,−1, 0, 1, 2, 3, 4, 5} defines the five-yearhorizon over which we study dynamics.19 The coefficients{ψ5,m, ψ<5,m}m∈M summarize trends in mean outcomes relative tothe date of an initial decision, which may differ by the firm’s exante patent value quintile. Of primary interest are the coefficients{τ5,m, τ<5,m}m∈M, which summarize the differential trajectory ofmean outcomes for initially allowed and initially rejected firmsby time relative to the initial decision for top-quintile and lower-quintile value observations, respectively.

Figure III plots the coefficients {τ5,m, τ<5,m}m∈M from equa-tion (7) for our main firm outcome variable, surplus. The estimatedcoefficients illustrate that, among firms with patent applicationsin the top quintile of the predicted value distribution, firms whoseapplications are initially allowed exhibit trends in surplus perworker similar to those whose applications are initially rejectedin the years prior to the initial decision. However, surplus perworker rises differentially for allowed firms in the wake of an

19. We “bin” the endpoint dummies so that D5jt is an indicator for the decision

having occurred five or more years ago and D−5jt is an indicator for the decision

being five or more years in the future.

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FIGURE III

Event Study Estimates: Surplus (EBITD + Wage Bill) per Worker

This figure plots the response of surplus per worker following an initial patentallowance, separately for high and low ex ante valuable patent applications, inour analysis sample. Regressions include art unit by application year by calendaryear fixed effects and firm fixed effects, as in equation (7). 95% confidence inter-vals were constructed from standard errors two-way clustered by (i) art unit and(ii) application year by decision year. The horizontal short-dashed red line (colorversion online) is the pooled difference-in-differences estimate of the impact ofwinning a valuable patent on surplus per worker from Table V. Surplus is EBITD(earnings before interest, tax, and depreciation) + wage bill. Q5 is quintile five ofpredicted patent value; <Q5 are the remaining four quintiles. Q5 coefficients areoffset from their integer x-axis value to improve readability.

initial allowance and remains elevated afterward.20 Firms withlower predicted value applications, by contrast, exhibit no de-tectable response of surplus per worker to an initial allowance.Figure IV documents similar patterns in our main worker out-come variable, wage bill per worker. As expected, the wage re-sponse to an initial allowance is muted relative to the surplusresponse; the ratio of these two impacts provides a crude estimateof the pass-through coefficient π of roughly one-third.

20. In the presence of employee turnover, the total number of W2 and 1099filings over the course of a year is likely to overstate employment at any point intime. This could lead to a (small) downward bias in our estimates of employmenteffects of patent allowances since retention rates increase (separation rates de-cline), thus also affecting “per W2 worker” outcomes. These effects are likely quitesmall, so in practice we are not concerned about this as a source of bias.

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FIGURE IV

Event Study Estimates: Wage Bill per Worker

This figure plots the response of wage bill per worker following an initial patentallowance, separately for high and low ex ante valuable patent applications, inour analysis sample. Regressions include art unit by application year by calendaryear fixed effects and firm fixed effects, as in equation (7). 95% confidence intervalswere constructed from standard errors two-way clustered by (i) art unit and (ii) ap-plication year by decision year. The horizontal short-dashed red line (color versiononline) is the pooled difference-in-differences estimate of the impact of winninga valuable patent on wage bill per worker from Table V. Q5 is quintile five ofpredicted patent value; <Q5 are the remaining four quintiles. Q5 coefficients areoffset from their integer x-axis value to improve readability.

While wages and surplus respond rather immediately to top-quintile initial allowances, Figure V reveals that firm size (asmeasured by the log number of employees) responds more slowly,taking roughly three years to scale to its new level. The fact thatearnings impacts remain stable over this horizon casts doubt onthe possibility that the impacts in Figure III are driven primarilyby an increase in hours worked (which we cannot observe in taxdata) rather than an increase in hourly wages. The nearly im-mediate response of surplus and wages to initial allowances maysignal that our panel of relatively small innovative firms was ini-tially credit constrained. Evidence from Farre-Mensa, Hegde, andLjungqvist (2017), who document that patent grants are stronglypredictive of access to venture capital financing, corroborates thisview. Access to venture capital and other forms of financing is

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FIGURE V

Event Study Estimates: log (employees)

This figure plots the response of the logarithm of employees per worker followingan initial patent allowance, separately for high and low ex ante valuable patentapplications, in our analysis sample. Regressions include art unit by applicationyear by calendar year fixed effects and firm fixed effects, as in equation (7). 95%confidence intervals were constructed from standard errors two-way clustered by(i) art unit and (ii) application year by decision year. The horizontal short-dashedred line (color version online) is the pooled difference-in-differences estimate of theimpact of winning a valuable patent on the logarithm of the number of employeesat the firm in thousands of people. Q5 is quintile five of predicted patent value;<Q5 are the remaining four quintiles. Q5 coefficients are offset from their integerx-axis value to improve readability.

a plausible additional channel through which patent decisionscould quickly affect the marginal revenue product of labor andconsequently worker wages.21

As background for interpreting the magnitude of these re-sults, Figure VI documents that an initial allowance raises theprobability of having the patent application granted by roughly50% in the year after the decision, with gradual declines after-ward. The probability of receiving a patent grant jumps by less

21. As a robustness check we fit a version of equation (7) allowing linearinteractions of D0

jt and I Aj · D0jt with the week of the patent decision. We find that

the contemporaneous surplus impacts we observe are increasing in the numberof days that have elapsed since the initial decision. We find no contemporaneouseffect of initial patent allowances decided in late December on either surplus orwages, which reassures us that the effect is not abnormally immediate.

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FIGURE VI

Event Study Estimates: Probability of Patent Grant

This figure plots the response of the probability of patent grant following aninitial patent allowance, separately for high and low ex ante valuable patent ap-plications, in our analysis sample. Regressions include art unit by application yearby calendar year fixed effects and firm fixed effects, as in equation (7). 95% con-fidence intervals were constructed from standard errors two-way clustered by (i)art unit and (ii) application year by decision year. The horizontal short-dashedred line is (color version online) the pooled difference-in-differences estimate ofthe impact of winning a valuable patent on the probability of the patent havingbeen granted. Q5 is quintile five of predicted patent value; <Q5 are the remainingfour quintiles. Q5 coefficients are offset from their integer x-axis value to improvereadability.

than 100% for two reasons. First, some initially allowed applica-tions are not pursued by applicants, possibly because the assigneewent out of business while awaiting the initial decision, or becausethe applicant learned new information since filing which led themto believe that the patent was not commercially valuable. Sec-ond, as described in Section IV, many initially denied applicationsreapply and eventually have their applications allowed. Our esti-mates in Figure VI suggest that the impact of initial allowanceson patent grants is somewhat smaller for higher-value patents,perhaps because they are more likely to be approved shortly af-ter a rejection; a pooled difference-in-differences estimate of theimpact on the grant probability of high-value patents is approxi-mately one-third. Hence, the impact of high-value patent grantson firm outcomes is likely to be roughly three times the impact of

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an initial allowance on firm outcomes, though it is possible thatallowances influence firm outcomes independent of grant status ifallowances relieve credit constraints before a patent has actuallybeen granted. In what follows, we continue to report the reduced-form impacts of allowances as our ultimate goal is to instrumentfor surplus rather than for patent grants.

VI.A. Impacts on Firm Averages

Table V pools pre- and post application years and quantifiesthe average effects displayed in the event study figures by fittingsimplified difference-in-differences models of the following form:

Yjt = α j + κt,k( j) + Q5 j · Postjt · (ψ5 + τ5 · I Aj

)(8)

+ (1 − Q5 j

) · Postjt · (ψ<5 + τ<5 · I Aj

) + rjt.

The parameters reported in Table V are τ 5 and τ<5, which respec-tively govern the effects of top-quintile and lower-quintile valuepatents being initially allowed.

Table V, column (1) documents that initial allowances haveno effect on the probability of firm survival, as proxied by the pres-ence of at least one W2 employee. Given this result, the remainderof the columns focus on outcomes conditional on firm survival asmeasured by the presence of at least one W2 employee (hence thesmaller sample sizes in subsequent columns). Column (2) reportsthe impact of an initial allowance on the log of firm size, as mea-sured by the number of W2 employees at the firm.22 Having atop-quintile patent allowed leads the firm to expand by roughly22%. Notably, initial allowances of patents with lower predictedvalue have no detectable impact on firm survival, firm size, or anyother outcome that we examine; these results suggest that dif-ferential trends for initially allowed and initially rejected patentsare unlikely to confound our analysis.

An allowance of a high-value patent application is associatedwith roughly $37,000 in additional revenue per worker (column(3)) and roughly $16,000 in value added per worker (column (4)).EBITD per worker rises by roughly $9,100 (column (5)), whichwe interpret as income to firm owners, while wage bill per em-ployee rises by roughly $3,700 (column (6)). Our surplus measure,

22. We work with logarithms for firm size because this variable is not win-sorized and is very heavily skewed.

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which sums EBITD and wage bill, rises by $12,400 per worker(column (7)).23 As described in Section III, we interpret our es-timated effects on surplus as the impact on total operating cashflow at the firm. In this article, our central interest is in estimat-ing how this surplus measure is divided between workers and firmowners.

Table V also reports impacts on various measures of la-bor compensation. A successful top-quintile patent applicationis associated with an increase in firm-level deductions for labor-related expenses of around $3,900 (Table V, column (8)), whichis roughly comparable to what we found for wage and salarycompensation based on W2 wage bills. On the other hand,pooling W2 earnings with 1099 earnings yields an impact ofonly $2,800 per worker (column (9)). In percentage terms,these impacts are fairly close: labor compensation per W2 risesby roughly 7.1%, while W2 + 1099 earnings per W2 rise by5.6%. However, these results suggest that 1099 compensationis, if anything, less responsive to shocks than W2 wages andsalaries.

Finally, the last column of Table V reports impacts on a mea-sure of the average individual income tax burden per worker.24

An initial allowance of a high-value patent is estimated to yield$770 of additional tax revenue per worker. Although this fig-ure is statistically indistinguishable from 0, the point estimateimplies an effective marginal tax rate of 21% on the $3,700 ofextra W2 earnings reported in Table V, column (6), which isroughly the average U.S. marginal tax rate found in TAXSIM (seeFeenberg and Coutts 1993) over our sample period.25 In per-centage terms, an initial allowance of a high-value patent raisestax revenue per worker by 4.3%—slightly below the proportionalimpact on W2 earnings per worker. This finding suggests the

23. The sum of the per worker impacts on EBITD and wage bill does not exactlymatch the impact on surplus per worker because the variables are winsorizedseparately.

24. Our measure, which is the main tax variable in the databank (the mainpanel data set used by researchers using the U.S. Treasury tax files), captures“tentative” tax burden before accounting for the alternative minimum tax. It isnot available in a small number of cases, which is why column (10) has slightlyfewer observations than the per W2 worker columns.

25. See http://users.nber.org/ taxsim/allyup/ally.html for annual estimates.

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http://users.nber.org/protect unhbox voidb@x penalty @M taxsim/allyup/ally.html


presence of an important fiscal externality between corporate taxtreatment of innovation and income tax revenue.26

Online Appendix Table D.3 repeats the impact analysis onthe subset of “closely held” firms registered as partnerships orS-corporations. Because these businesses rarely offer stock com-pensation, wage responses are likely to provide a more compre-hensive measure of rent sharing in this subsample (see Smithet al. 2019). Among closely held firms we find somewhat largereffects on revenue, value added, and EBITD per worker accom-panied by commensurately large impacts on average wages andlabor compensation. In our pooled sample, the ratio of the impacton wage bill per worker to the impact on surplus per worker is29 cents, whereas the ratio at closely held firms is 27 cents; theclose similarity of these two estimates suggests that the inabilityto offer stock options does not dramatically alter the pass-throughfrom firm-specific shocks to worker wages. Online AppendixTable D.4 shows that patent allowances also have similar effectson firms in the top and bottom half of the distribution of initialfirm sizes.

VI.B. Impacts on Workforce Composition

A difficulty with interpreting impacts on firm-level ag-gregates is that firms may alter the skill mix of their em-ployees in response to shocks, in which case impacts onaverage wages could simply reflect compositional changesrather than changes in the compensation of similar em-ployees. Van Reenen (1996, 216–217) provided a back-of-the-envelope calculation suggesting that compositional changeswere unlikely to be a major concern in his sample. InTable VI we directly investigate the possibility of such compo-sitional changes using our link of W2’s to EINs.

Table VI, columns (1) and (2) reveal that neither theshare of employees who are women nor the share of employ-ees who are inventors changes appreciably in response to anallowance. We also find little evidence that the quality of newhires (“entrants”), as proxied by their earnings in the year prior

26. One specific implication of this finding is that patents influence the revenueraised from both business and individual income taxes. Consequently, so-calledpatent box proposals, which are designed to exempt the rents associated withpatent grants from business taxes, are likely also to impact the revenue collectedfrom individual income taxes.

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to hiring (column (3)), rises in response to an initial patentallowance. Likewise, the earnings of those workers who choose toseparate from the firm appear to be unaffected by the allowance(column (4)).

Examining “firm stayers” who were present in the year ofapplication and continued to be employed by the firm provides adifferent window into potential changes in workforce composition.We find no appreciable effect on the application year earnings ofstayers (Table VI, column (5)), suggesting little change in the qual-ity of retained workers. Finally, the average age of W2 employeesdrops by roughly a year in response to a valuable patent allowance(column (6)), which is in keeping with our finding that firms growin response to valuable allowances and the fact that job mobilitydeclines with age (Farber 1994).

Columns (7) and (8) report impacts on a pair of indices ofworker “quality.” Each index gives the firm’s average in that yearof the predicted log earnings of its employees. The first indexforms predictions from a regression of individual log W2 earningson a quartic in age fully interacted with gender and inventor sta-tus plus controls for tax year fixed effects (which are not usedto form the prediction). The second index adds a polynomial inworkers’ earnings on the previous job as a predictor along with anindicator for whether this is the worker’s first job. Effects on bothquality measures are statistically indistinguishable from 0. Takentogether, these results provide no evidence of skill-upgrading re-sponses and hint that mild skill downgrading (primarily throughage declines) is a more likely possibility.

VI.C. Impacts on Within-Firm Inequality

Figure VII analyzes the impact of initial allowances on vari-ous measures of within-firm inequality. The underlying estimatesused to construct these figures are reported in Online AppendixTables D.5 and D.6. Consistent with the literature on genderdifferences in rent-sharing (e.g., Black and Strahan 2001; Card,Cardoso, and Kline 2016), we find that initial allowances exacer-bate the gender earnings gap. While male earnings rise by roughly$5,900 (or roughly 9%; Online Appendix Table D.5, column (1)) inresponse to a valuable patent allowance, female earnings appearunresponsive to initial allowances (Online Appendix Table D.5,column (2)). Among firms that employ both genders, the genderearnings gap increases by roughly $6,900 in response to a valu-able initial allowance, or roughly 25% (Online Appendix Table D.5,column (3)).

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FIGURE VII

Within-Firm Inequality

This figure reports difference-in-differences coefficient and percent impact esti-mates of the effect of initial patent allowances on within-firm inequality measures,for high ex ante valuable patent applications, in our analysis sample. Point esti-mates in the “Coefficients” panel correspond to coefficients on interactions of thedesignated value category with a postdecision indicator and an indicator for theapplication being initially allowed. Controls include main effect of value categoryinteracted with a postdecision indicator, firm fixed effects, and art unit by applica-tion year by calendar year fixed effects, as in equation (8). 95% confidence intervalswere constructed from standard errors two-way clustered by (i) art unit and (ii)application year by decision year. “Percent Impacts” point estimates correspondto the percent change in the outcome variable at the outcome variable’s mean forwinning a patent allowance for a high ex ante valuable patent application. Someconfidence intervals were truncated to ease visualization. Officers’ earnings arederived from each firm’s tax filings, where firms are required to list officer andnonofficer pay. Quartiles refer to within-firm wage quartiles (e.g., “Q1 earnings”measures the average wage bill in within-firm wage quartile one). Earnings aremeasured in thousands of 2014 dollars.

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The earnings gap between inventors and noninventors alsowidens in response to an initial allowance. Online AppendixTable D.5, column (4) shows that the earnings of inventors riseby roughly $16,900 in response to an initial allowance. The earn-ings of noninventors rise by only around $2,200. Focusing on firmsthat employ both inventors and noninventors, we find that theinventor-noninventor earnings gap increases by roughly $14,900in response to a valuable initial allowance, or roughly 17% (OnlineAppendix Table D.5, column (6)). The gender and inventor gapsare overlapping, but not identical phenomena. Figure VII showsthat the earnings of noninventor males rise by roughly $4,000—less than all men, but more than all noninventors.

Another important within-firm contrast is between firm of-ficers and other workers. All U.S. businesses are required to listofficer pay separately from the pay of nonofficers when filing taxes.Officers are employees who have the authority to delegate tasksand to hire employees for the jobs that need performing, and typ-ically correspond to high-level management executives. We findthat an initial allowance raises average officer earnings per W2employee by roughly $3,700, enough to explain the entire W2 earn-ings response reported in Table V. By contrast, nonofficer earningsexhibit no appreciable response to initial allowances, though wecannot rule out small increases. As shown in Online AppendixTable D.8, the components of labor compensation other than offi-cer earnings also fail to respond to patent allowances, suggestingthat profit-sharing and employee benefit programs do not respondstrongly to patents.

Finally, to provide a composite measure of within-firm earn-ings inequality, we break workers in each firm-year with at leastfour W2s into quartiles based on their annual earnings. We find noeffect of an initial allowance on the average earnings of workersin the bottom three quartiles of the firm-specific earnings distri-bution, but the mean earnings of top-quartile workers rises byroughly $8,100 per worker. The pay gap between top and bot-tom quartile workers rises by roughly the same amount (OnlineAppendix Table D.5, column (9)).

VI.D. Impacts on Earnings by Timing of Worker Entry and Exit

Our results in Section VI.B suggested that initial allowancesare not associated with major changes in workforce composition.However, an alternative way to hold constant the quality of the

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workforce is to study the impact of a patent allowance on theearnings of a fixed cohort of workers.

Table VII, column (1) documents that the average earnings ofthe cohort of workers present in the year of the patent applicationrise by roughly $4,000 or about 7% in response to an initial al-lowance. These effects are concentrated in the subset of the cohortthat remains with the applicant firm (“stayers”), whose earningsare estimated to rise by $7,800 (around 11%) a year in responseto an initial allowance (column (2)). Members of the applicationcohort who leave the firm, by contrast, have earnings that fall sta-tistically insignificantly in response to an initial allowance (col-umn (3)). The concentration of earnings effects on stayers castssome doubt on reputational (or “career concerns”) explanationsfor firm-specific wage fluctuations (Harris and Holmstrom 1982;Gibbons and Murphy 1992; Holmstrom 1999), as firm leavers ap-pear to be unable to transport their patent-induced wage gains tonew employers.

The model of Section II interpreted wage fluctuations as rentsharing with incumbent workers. Consistent with that model,we find an economically small and statistically insignificant ef-fect of initial allowances on the average earnings of entrants(Table VII, column (4)). Given our finding in Section VI.B thatthe composition of entrants does not seem to have changed inresponse to initial allowances, the discrepancy between our mea-sured impacts of initial allowances on the earnings of entrants andon the earnings of firm stayers suggests that the order in whichworkers are hired plays an independent role in the transmissionof firm shocks to wages.27 Online Appendix Table D.4, column (10)shows that the differential earnings response of firm stayers topatent allowances is not confined to small firms.

As mentioned in Section II, some dynamic models (e.g.,Postel-Vinay and Robin 2002) can generate a drop in entry wagesin response to a firm productivity increase because wage growthrates increase. Such an elevation of wage growth rates shouldeventually affect earnings levels. However, Table VII, column (5)reveals a negative (“wrong-signed”) and statistically insignificantimpact of initial allowances on the earnings of workers hiredwithin the past three years. A shift in growth rates, in conjunctionwith stable entry wages, should also lead to an escalating pattern

27. Related work by Buhai et al. (2014) shows that worker seniority exerts anindependent effect on wages even after netting out firm-wide shocks.

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of pooled wage impacts. However, we saw in Figure IV that wageimpacts are roughly stable after the initial decision. Hence, weconclude there is no evidence of a permanent impact on earningsgrowth rates.28

Table VII, columns (6)–(8) adjust for possible compositionalchanges by subtracting from the various earnings measures anaverage earnings level of the same group of workers in the year ofapplication, which adjusts for any time-invariant heterogeneity inworker quality. Column (6) (which can be compared to column (2))shows that subtracting the average application year earnings ofthe firm stayers has little effect on the estimates. The estimates incolumns (7) and (8) (analogous to columns (3) and (4)) remain sta-tistically equal to 0, suggesting that these other groups’ earningsare relatively insensitive to the patent decision.

Finally, Figure VIII reports impacts of high-value initial al-lowances on the average earnings of various groups of firm stay-ers. Initial allowances exacerbate the gender earnings gap amongstayers, but the impacts on the earnings of female stayers are nowestimated to be positive at around $2,700. Online Appendix TableD.7 shows that the impact of an initial allowance on the earn-ings gap between male and female firm stayers is roughly $8,900(around 24%) and statistically distinguishable from 0. As a pointof comparison, we find that the earnings of male firm stayersrespond roughly 2.9 times as much as their female colleagues,which is slightly below the corresponding ratio of 4 found byBlack and Strahan (2001) in their study of banking deregula-tion using firm aggregates. Likewise, earnings of inventor-stayersare estimated to increase by far more than those of noninven-tors. However, the estimated impacts on noninventor stayersare clearly distinguishable from 0 and amount to a roughly9% increase. This responsiveness of noninventor earnings butlarger response of inventor earnings echoes the findings presentedin contemporaneous work by Aghion et al. (2018), which esti-mates that in Finnish firms inventor earnings are around twiceas responsive to patent application filings as are noninventorearnings.

28. We have also directly computed impacts on earnings growth rates forworkers hired within the past three years, but this led to highly imprecise esti-mates. Specifically, we estimate an impact of −1 percentage point on the three-yeargrowth rate of the earnings of new hires, with a standard error of 7 percentagepoints.

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FIGURE VIII

Within-Firm Inequality among Stayers

This figure reports difference-in-differences coefficient and percent impact esti-mates of the effect of initial patent allowances on within-firm stayer inequalitymeasures, for high ex ante valuable patent applications, in our analysis sample.Stayers are defined as those who were employed by the same firm in the year ofapplication. Point estimates in the “Coefficients” panel correspond to coefficientson interactions of the designated value category with a postdecision indicator andan indicator for the application being initially allowed. Controls include the maineffect of value category interacted with a postdecision indicator, firm fixed effects,and art unit by application year by calendar year fixed effects, as in equation (8).95% confidence intervals were constructed from standard errors two-way clusteredby (i) art unit and (ii) application year by decision year. Some confidence intervalswere truncated to ease visualization. Quartiles refer to within-firm wage quartiles(e.g., “Q1 earnings” measures the average wage bill in within-firm wage quartileone). Earnings are measured in thousands of 2014 dollars.

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The bottom of Figure VIII reports impacts on average earn-ings by the worker’s position in the firm’s earnings distribution atthe time of the patent application. Large earnings gains, amount-ing to roughly 6–8% increases, are present for firm stayers ini-tially in the top half of the firm-specific earnings distribution. Inour estimation sample, firms with high-value patents have, in anaverage year, roughly 10 stayers in the top initial earnings quar-tile and 9 in the third quartile. Because earnings impacts areclearly present among third-quartile workers, our pooled impactson stayer earnings are unlikely to solely represent the capture ofrents by CEOs or other top executives. By contrast, the earningsresponse of firm-stayers initially in the bottom half of the distri-bution exhibit relatively muted responses, that are statisticallyindistinguishable from 0.

VII. PASS-THROUGH ESTIMATES

Table VIII reports rent-sharing specifications based on equa-tion (5) that relate earnings outcomes to surplus per worker. Asdiscussed in Section III.D, our preferred approach uses the sumof wages and EBITD to measure surplus. However, for compar-ison with past literature, we also report specifications proxyingsurplus with our measure of value added.

Panel A, column (1) shows that regressing the average wagebill per worker on our preferred measure of surplus per worker,together with our standard set of (firm and art unit by appli-cation year by calendar year) fixed effects yields an estimatedpass-through coefficient π of 0.16. Instrumenting surplus withthe interaction of a postdecision indicator and an indicator for theapplication being initially allowed increases the estimated coef-ficient to 0.29, implying that workers capture 29 cents of eachadditional dollar of surplus. Because our first-stage F statistic isnear the benchmark of 10, we also provide a weak-identificationrobust confidence interval, which reveals that we can reject valuesof π below 0.1 or above 0.57 at the 10% level.29 For comparison

29. These confidence intervals, which are two-way clustered on art unit andapplication year by decision year, employ the minimum distance variant of theAnderson-Rubin test statistic (Anderson and Rubin 1949) described in section 5.1of Andrews, Stock, and Sun (2018). The endpoints of the confidence interval aredefined by quadratic inequalities, which we solved analytically. We thank LiyangSun for suggesting this approach.

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1390 THE QUARTERLY JOURNAL OF ECONOMICST

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with the prior literature, we convert our estimates of π to elas-ticities using the means of surplus and wages among firms withtop quintile patent applications. While OLS estimation yields apass-through elasticity of 0.19, IV yields an estimated elasticityof 0.35. A plausible candidate explanation for the larger IV es-timates is that wages respond more strongly to lower frequencyfluctuations in surplus (Guiso, Pistaferri, and Schivardi 2005);however, in Online Appendix Table D.9 we document that usingthree-year averages of surplus yields only modest increases inOLS estimates of π , which continue to rise dramatically wheninstrumented.

Panel B, columns (1) and (2) show the corresponding resultswhen value added per worker is treated as the endogenous vari-able. This yields lower pass-through coefficients, which is in keep-ing with the notion that value added includes a number of ex-traneous cost components that cannot be captured by workers. Inelasticity terms, however, using value added yields larger elas-ticities because value added has a greater mean than our pre-ferred surplus measure. A useful point of comparison comes fromVan Reenen (1996), who reports an elasticity of average wageswith respect to quasi-rents of 0.29 (Table III, second row). Cardet al. (2018) suggest doubling quasi-rent elasticities to make themroughly comparable to a value-added elasticity. Applying this ruleof thumb to Van Reenen’s study yields a value-added equivalentelasticity of 0.58, which is slightly above our instrumented value-added elasticity estimate of 0.47. On the other hand, our value-added pass-through coefficient of 0.23 is directly comparable to thefirm-level pass-through estimates of Abowd and Lemieux (1993)who report an identical pass-through coefficient of 0.23 (Table III,column (8)).

Table VIII, Panel A, columns (3)–(6) change the dependentvariable to be the earnings of various subgroups of workers em-ployed by most firms.30 OLS estimates indicate that the earningsof men are slightly more sensitive to surplus fluctuations than theearnings of workers in general. However, instrumenting surpluswith initial allowances dramatically raises this point estimate, in-dicating that men capture 53 cents of every dollar of surplus perworker, roughly 80% higher than was found for the pooled esti-mate. By contrast, noninventor earnings responses are relatively

30. Table VIII omits estimates for subgroups (e.g., female inventors) that havesample sizes too small to produce reliable estimates.

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muted, indicating such workers capture only 19 cents of everydollar of surplus per worker.

Table VIII, Panel A, columns (7) and (8) restricts attentionto firm stayers, who were present in the year of application. OLSestimates indicate that stayer earnings are more sensitive to sur-plus fluctuations in levels (relative to the sample of all workers),but the elasticity is the same as that found for the average earn-ings of all workers (0.19). Instrumenting the surplus changes thisconclusion dramatically: stayers are estimated to capture 61 centsof every dollar of surplus, with a corresponding elasticity of 0.56.Remarkably, the 90% confidence interval for π in this subgroupranges from 0.21 to 1, indicating that we cannot reject that firmstayers capture the entirety of their replacement costs in higherearnings. Columns (9) and (10) adjust stayer earnings for potentialchanges in workforce composition by subtracting off their earningsin the application year, which should difference out any selectionon time-invariant worker skills. As expected given our results inSection VI.B, this adjustment has minor effects on the results—lowering, for instance, the instrumented pass-through of surplusto earnings from 61 cents to 51 cents on the dollar.

Finally, columns (11) and (12) show that our pass-throughresults are not driven exclusively by workers listed as inventorson patent applications: the instrumented value of π among non-inventor stayers is 0.48. Though the standard errors for column(12) are somewhat smaller than the estimates in column (8), thefirst stage is somewhat weaker, which leads the lower limit ofthe 90% confidence interval for π among noninventor stayers tobe nearly identical to that of all stayers. Because most previousstudies of rent-sharing do not focus on innovative firms, this esti-mate is arguably most comparable to the work reviewed in Cardet al. (2018).

In sum, we find that the earnings of workers, particularlythose who were present in the year of application, are quite sensi-tive to fluctuations in surplus. On average, a $1 increase in surplusis estimated to yield a 29 cent increase in worker earnings anda 61 cent increase in the earnings of firm stayers. Using valueadded instead of our preferred surplus measure yields uniformlylower pass-through estimates but tends to raise elasticities sub-stantially. In elasticity terms, our pooled estimates are larger thanthe bulk of recent studies reviewed by Card et al. (2018) but alignclosely with the estimates of Abowd and Lemieux (1993) and VanReenen (1996) which exploit firm aggregates.

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Our finding of larger elasticities may be partly attributableto our use of external instruments. Abowd and Lemieux (1993),Van Reenen (1996), and Garin and Silverio (2017) all find thatinstrumenting value added yields large increases in rent-sharingestimates. Garin and Silverio (2017) estimate a pooled elasticityof 0.15 (their table 6, column 4) in Portuguese data using exposureto exchange rate shocks as an instrument, and find a much largerelasticity of 0.28 (their table 9, column 2) in industries with lowseparation rates. Because measuring the level of surplus is par-ticularly difficult at small firms, we are somewhat less confidentin our elasticity estimates than we are in the more theoreticallymotivated pass-through coefficients, which are robust to mismea-surement of the level of surplus. Nevertheless, our 90% confidenceinterval for π permits corresponding surplus elasticities as low as0.19 for firm stayers.31

Another plausible explanation for finding strong earningssensitivity to surplus shocks is our focus on innovative firms,which are likely to rely heavily on the specific human capitalof their workforce. This interpretation is consistent with the find-ings of Van Reenen (1996), who also studied innovative firms. Ourfinding of very large wage pass-through to early cohorts of workersis consistent with the notion that early employees, some of whommay be founders, are particularly difficult for firms to replace.

VIII. RETENTION ESTIMATES

The wage-posting model of Section II interpreted earningsresponses to firm-specific shocks as attempts to retain incumbentworkers. Figure IX provides event study estimates of the impactof patent allowances on the logarithm of the fraction of the ap-plication cohort working at the firm, split by whether the workerwas in the top or bottom half of the firm-specific earnings dis-tribution in the year of application. Recall from Figure VIII thatthe earnings responses to initial allowances were concentrated inthe top half of the distribution of firm stayers. Consistent withthe notion that these earnings movements capture rent shar-ing, the retention of “above median” firm stayers (right panel of

31. This figure comes from multiplying the lower limit of the confidence in-terval for π , which is 0.21, by the ratio of elasticity to the pass-through coefficientfor mean stayer wages among firms with high-value patent applications, which is0.560.61 ≈ .92 (see Table VIII, column (8)).

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FIGURE IX

Event Study Estimates: Employee Retention Rate by Application Year Earnings

This figure plots the response of log retention rate following an initial allowance,separately for high and low ex ante valuable patent applications, in our analysissample. Regressions include art unit by application year by calendar year fixedeffects and firm fixed effects, as in equation (7). 95% confidence intervals wereconstructed from standard errors two-way clustered by (i) art unit and (ii) appli-cation year by decision year. “Below median wage workers” and “Above medianwage workers” respectively refer to members of the application cohort who earnedbelow and above that firm’s median in the application year. Q5 is quintile five ofpredicted patent value; <Q5 are the remaining four quintiles. Q5 coefficients areoffset from their integer x-axis value to improve readability.

Figure IX) responds strongly to initial allowances while the reten-tion of “below median” stayers (left panel of Figure IX) exhibits avery weak and statistically insignificant response to allowances.Interestingly, the retention response stabilizes by three years af-ter the initial decision date. This pattern suggests the earningsresponse, which from Figure IV manifests rather quickly, servesto retain incumbent workers who would have otherwise separatedover the first three years after an initial rejection.

Table IX scales the retention responses of various groups ofworkers present in the application year by the impact on theirlog earnings to obtain IV estimates of the incumbent retention-wage elasticity. Instrumenting stayer wages with the initial al-lowance decision yields an estimated retention-wage elasticity of1.2, or equivalently, a separation-wage elasticity of −1.6. This esti-mate is well within the range of separation elasticities reported inManning’s (2011) review of quasi-experimental studies but issomewhat larger in magnitude than the short-run elasticities

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reported in Dube, Giuliano, and Leonard (2018). However, Dube,Giuliano, and Leonard (2018) report nine-month elasticities,whereas we interpret our estimates as representing three-yearelasticities, which we would expect to be a bit larger. Despitea first-stage F statistic below the benchmark of 10, our weak-identification robust confidence interval indicates that we can re-ject retention elasticities below 0.46 at the 10% level.

We find little evidence of heterogeneity in the retention elas-ticity, although our analysis is hampered by a weak first stagefor some subgroups. Among “above median” stayers, the reten-tion elasticity rises slightly to 1.4, but we cannot reject that theelasticity is the same as in the pooled sample, which is in keep-ing with the notion that the pooled results are driven primar-ily by the above-median stayers. We do not report estimates forbelow-median stayers because the first stage is extremely weak,which leads to erratic estimates. Male retention elasticities are es-timated to be somewhat below female elasticities, but the femaleestimates are imprecise to the point of being indistinguishablefrom 0. Finally, noninventors are estimated to have a retentionelasticity of 1.3, nearly identical to what we found in our pooledanalysis. The finding of a stable retention elasticity across groupsreinforces the evidence in Figure IX that the groups experiencingthe largest earnings responses also exhibit the largest retentionresponses. This corroborates our model-based interpretation ofthe earnings impacts we measure as reflecting economic rents, aview we consider in more quantitative detail in Section IX.

IX. MODEL-BASED INTERPRETATION

In the model of Section II, the retention wage elasticity canbe written:

d ln G(wI

j

)d ln wI

j

= ηwI

j

wIj − wm

j

= η

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wmj

wIj

wmj

− 1.

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j

wmj

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j . Bycontrast, workers who have been at the firm for four or more years

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earn roughly $79,000, which we take as a measure of wIj . Hence,

we calibratewI

j

wmj

= 7943.5 ≈ 1.8.

In Table IX, we found a pooled retention elasticity of approxi-mately 1.2. Hence, our estimate of η is 1.2 × 1.8

0.8 ≈ 2.7. Recall fromequation (3) that in the model of section II workers are offered afraction θ = η

1+ηof their marginal replacement costs as a wage pre-

mium. Our retention elasticity estimate therefore implies that in-cumbent workers capture roughly 73% of their replacement costsin wage premia.

We can also use our estimates to quantify these marginal

replacement costs. Rearranging equation (3), we havec′

( NjIj

)wm

j=[

wIj

wmj

−1

]θ

= 0.80.73 ≈ 1.1. Hence, our calibration suggests that the

marginal replacement cost of an incumbent worker is roughlyequal to the annual earnings of a new hire. This replacementcost estimate is higher than is usually found in simple linear-quadratic models of employment adjustment (Hamermesh andPfann 1996; Bloom 2009; Cooper and Willis 2009). However, westudy fairly large shocks to small firms which, with convexity inhiring/training costs, should lead to correspondingly large replace-ment costs on the margin.

We can also use our estimates to compute an implied elastic-ity of product demand ε. In Table VIII we found that incumbentworkers captured 61 cents of every dollar of patent-induced sur-plus. Taking π = 0.61 = (

ε−1ε

)θ and using our estimate of θ = 0.73

implies that ε ≈ 6.0, which corresponds to a 20% markup of prod-uct price over marginal cost. This finding is in line with recentwork that has used values of ε ranging from 4.5 (Suarez Serratoand Zidar 2016) to 7 (Coibion, Gorodnichenko, and Wieland 2012).

Online Appendix Table D.10 reports some alternative cali-brations of model inputs that set the pass-through and retentionelasticities to different values along with the incumbent wage pre-mium. Interestingly, some calibrations yield invalid values of thestructural parameters, indicating that our model can be used torule out some configurations of parameters falling within our con-fidence intervals. The general theme of this sensitivity exercise isthat across a wide range of potential rationalizations of the data,workers capture a large fraction of their marginal replacementcosts in wage premia and that those costs are substantial.

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It is worth remarking briefly on how our model rational-izes the gender differences in earnings pass-through reported inFigure VIII. The model suggests two possible explanations forthese differences. A first potential explanation is that men andwomen might face different distributions of outside offers, whichwould manifest in different retention elasticities and conse-quently different pass-through coefficients. However, the resultsof Table IX provide little support for this conjecture. If anything,women exhibit slightly higher retention elasticities than men,which should yield greater earnings pass-through for them.

A second potential explanation for gender differences in earn-ings pass-through is that the marginal replacement costs of mencould—on average—exceed those of women. Concentration ofwomen in occupations involving smaller training and recruitingcosts, for example, could plausibly generate such differences. Re-call that earnings impacts are concentrated among firm “officers”who are probably difficult to replace because of the specific cap-ital embedded in their relationships with subordinate workers.Unfortunately, because of how officer earnings are reported (asaggregates in the firm-level data, rather than as a variable in ourworker micro-data) we do not know what fraction of officers arewomen. However, for the average firm in our sample, the fractionof women in the top quartile of its earnings distribution in the yearof initial patent application is only 11.5%, a fact that is consistentwith a broad range of evidence suggesting that U.S. women tend tobe employed in lower-paying occupations than men (Goldin 2014).

X. CONCLUSION

This article analyzes how patent-induced shocks to labor pro-ductivity propagate into worker earnings using a new linkage ofU.S. patent applications to U.S. business and worker tax records.Our baseline estimates suggest that on average every patent-induced dollar of surplus yields roughly 30 cents of additionalearnings; this share is roughly twice as high for incumbent work-ers present since the year of application. Among noninventorspresent since the year of application, who are arguably the groupmost comparable to the recent studies reviewed by Card et al.(2018), we find a both a pass-through rate and elasticity of roughly0.5. These estimates provide some of the first evidence, along withJager (2015), that truly idiosyncratic variability in firm perfor-mance is an important causal determinant of worker pay. Given

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that firm productivity is highly variable and persistent (Luttmer2007; Foster, Haltiwanger, and Syverson 2008), it is plausible thatfirm-specific shocks contribute substantially to permanent earn-ings inequality among identically skilled workers.

We document several sources of heterogeneity in the pass-through of patent-induced shocks to workers. First, patent al-lowances have no effect on the earnings of new hires. This findingmay be specific to the small firms we study, which are unlikelyto exhibit market power over new hires. Nevertheless, this find-ing implies that patent shocks “stretch” the firm’s pay scale byincreasing inequality between new hires and incumbent workers.Second, among incumbent workers, patent allowances exacerbatethe within-firm gender earnings gap. The gender differences inearnings pass-through found here are larger than those estimatedby Card, Cardoso, and Kline (2016) and Garin and Silverio (2017)in Portuguese data, but smaller than those reported by Black andStrahan (2001) in U.S. data. Third, while the earnings of bothinventors and noninventors respond to patent decisions, the earn-ings of inventors are substantially more responsive, which is no-table because previous studies of pass-through to inventors havestudied settings where inventor compensation is mandated bylaw.32 Finally, earnings impacts are strongly concentrated amongemployees in the top quartile of the within-firm earnings distri-bution, among firm officers, and among firm stayers initially inthe top half of the earnings distribution.

Two aspects of these heterogeneous earnings estimates areworth emphasizing. First, these effects appear to mirror hetero-geneity in the costs of replacing different types of workers. Sub-stituting new hires for high-skilled incumbents is particularlydifficult. Our retention results corroborate this view: worker re-tention rises most strongly among groups of workers with thelargest earnings increases. This pattern suggests, via revealedpreference, that these earnings fluctuations constitute economicrents. A quantification of our model finds that incumbent workerscapture the majority of their replacement costs in wage premia.The pairing of incumbent rents of this magnitude with stable

32. For example, Aghion et al. (2018) analyze how inventor and noninventorearnings change before and after patent applications among Finnish firms, butFinland, like many other European countries, has a law that requires firms to payinventors for inventions produced while they are employed. See the discussion inToivanen and Vaananen (2012).

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new-hire earnings highlights the importance of seniority and spe-cific investments in wage determination—themes emphasized by,among others, Becker (1964), Stevens (1994), and Manning (2006).Second, our findings strongly suggest that firm shocks play an im-portant role in generating earnings inequality not only across butalso within workplaces. Understanding the extent to which het-erogeneity in pass-through across workers contributes to overallearnings inequality is an important topic for future research.

UNIVERSITY OF CALIFORNIA, BERKELEY

U.S. DEPARTMENT OF THE TREASURY

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

PRINCETON UNIVERSITY

SUPPLEMENTARY MATERIAL

An Online Appendix for this article can be found at TheQuarterly Journal of Economics online. Code replicating tablesand figures in this article can be found in Kline et al. (2019), inthe Harvard Dataverse, doi:10.7910/DVN/HMFYON.

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